CN106896351A - A kind of radar network composite Poewr control method based on non-cooperative game - Google Patents

Abstract

The invention discloses a kind of radar network composite Poewr control method based on non-cooperative game, belong to Radar Signal Processing Technology field.This method is according to priori, the RCS of propagation loss and target relative to each radar in acquisition system between each radar and target；Then, under conditions of certain target acquisition performance is met, radar transmission power is minimized, sets up the radar network composite Power control model based on non-cooperative game, and model is solved by classical Lagrangian Relaxation Algorithm.Through iterative calculation, it is chosen at and meets under target acquisition performance condition so that the minimum performance number of each radar transmission powerAs optimal solution, you can obtain meeting the Radar Network System minimum total emission power of constraints.The present invention had both reduced the interference between different radars in Radar Network System, while improve the radio frequency Stealth Fighter of system in the case where certain target acquisition performance is met.

Description

A kind of radar network composite Poewr control method based on non-cooperative game

Technical field

The present invention relates to a kind of radar network composite Poewr control method based on non-cooperative game, belong to Radar Signal Processing skill Art field.

Background technology

Radar Network System refers to strange land to be disperseed into the multi-section emitter of deployment by specific procotol and equipment, is connect Receipts machine and Hub connect into organic whole, realize that time domain, frequency domain, spatial domain cooperate, and complete to target reconnaissance, visit The comprehensive integrated electronic information of the functions such as survey, information acquisition, recognition and tracking, firepower guiding.

However, increasingly sophisticated with current Battle Field Electromagnetic, Passive Detention System causes that the living environment of radar is received Serious threat and challenge is arrived.Radio frequency stealth technology refers to the active electronics such as radar equipment confrontation enemy's Passive Detention System Intercept and capture, sorting, identification, the stealth technology of tracking, with reduce engagement range that Passive Detention System equip to radio frequencies such as radars, section Probability is obtained for target, the battlefield survival and fighting efficiency of radar and its carrying platform can be further improved.When radar group When net system is detected to target, in the case where target acquisition performance is not influenceed, the global radiation of Radar Network System is reduced Power, can effectively improve the radio frequency Stealth Fighter of system, improve its battlefield survival.

When the Radar Network System that consideration works in same frequency range carries out target acquisition, how certain target acquisition is being met The total radiant power that Radar Network System is reduced in the case of performance is prior art problem demanding prompt solution.

The content of the invention

The present invention proposes a kind of radar network composite Poewr control method based on non-cooperative game, it is considered to work in same frequency When the Radar Network System of section carries out target acquisition, Radar Network System is reduced in the case where certain target acquisition performance is met Total radiant power, the radio frequency Stealth Fighter of lifting system.

The present invention is adopted the following technical scheme that to solve its technical problem：

A kind of radar network composite Poewr control method based on non-cooperative game, comprises the steps of：

(1) channel propagation impairments between each radar and target in Radar Network System are obtained, its mathematical description is：

Wherein,It is i-th transmitter antenna gain (dBi) of radar,It is i-th receiving antenna gain of radar,For With respect to i-th RCS of radar, λ is radar emission signal wavelength, R to target_iFor between i-th radar and target Distance, N_tIt is radar number in system；

(2) according to the investigative range for specifying SINRWherein：It is Signal to Interference plus Noise Ratio SINR value lower limit, It is the Signal to Interference plus Noise Ratio SINR value upper limit, sets up the radar network composite Power control model based on non-cooperative game：

Wherein, s.t. represents optimization object function " being limited to " following restrictive condition, u_i(p_i,p_-i) it is the effectiveness of radar i Function, p_iIt is the transmission power level of radar i, p_-iRepresent the radiant power of every other radar in the external system except radar i, b_iFor Penalty factor,Represent the maximum radiated power of radar i, i-th Signal to Interference plus Noise Ratio γ of radar_iCan be represented by the following formula：

Wherein, c_i,jRepresent the cross-correlation coefficient between radar i and radar j, σ²It is system noise power, p_jIt is radar j's Transmission power level,Represent the channel propagation impairments between radar i and radar j, d_i,jTable Show the distance between radar i and radar j, b_iIt is penalty factor, whenWhen, b_iKeep constant, whenWhen,WhenWhen,

(3) by utility function u_i(p_i,p_-i) to radiant power p_iSeek first-order partial derivative：

Wherein：u_i(p_i,p_-i) it is the utility function of radar i；

(4) by orderObtain the radiant power iteration expression formula of each radar in Radar Network System For：

Wherein：It is the radar i transmission power levels that nth iteration is calculated,It is (n+1)th thunder of iterative calculation Up to i transmission power levels,For the radar i Signal to Interference plus Noise Ratio values that nth iteration is calculated.

Beneficial effects of the present invention are as follows：

The present invention had both reduced the interference between different radars in Radar Network System, while meeting certain target acquisition The radio frequency Stealth Fighter of system is improve in the case of performance.

Brief description of the drawings

Fig. 1 is flow chart of the invention.

Specific embodiment

The invention is described in further details below in conjunction with the accompanying drawings.

1st, channel propagation impairments and target RCS (Radar Cross Section, RCS) are determined：

The present invention proposes a kind of radar network composite Poewr control method based on non-cooperative game.It make use of each radar and mesh The prioris such as the RCS of propagation loss and target relative to each radar between mark, therefore, should first determine each radar and target Between propagation loss and target relative to each radar RCS.It is assumed that working in the Radar Network System model of same frequency range As shown in Figure 1.

2nd, the radiation parameter and target acquisition SINR (Signal-to-Interference- of Radar Network System are determined Plus-Noise Ratio, Signal to Interference plus Noise Ratio) parameter such as scope：

According to the demand of radio frequency Stealth Fighter, it is assumed that i-th transmitter antenna gain (dBi) of radar and connect in Radar Network System Antenna gain is received to be respectivelyIts maximum radiated power isAdditive white Gaussian noise work(at radar receiver Rate is σ², according to the target acquisition SINR scopes that specified SINR is calculatedWherein：It is Signal to Interference plus Noise Ratio SINR value lower limit,It is the Signal to Interference plus Noise Ratio SINR value upper limit.

3rd, the radar network composite Power control model of non-cooperative game is built, and determination meets target acquisition SINR scopesMinimum total emission powerExpression formula：

Requirement according to Radar Network System to target acquisition performance, sets up the radar network composite power based on non-cooperative game The Mathematical Modeling of control, it is as follows：

In formula, s.t. represents optimization object function " being limited to " following restrictive condition, u_i(p_i,p_-i) it is radar i's Utility function, p_iIt is the transmission power level of radar i, p_-iThe radiant power of every other radar in the external system except radar i is represented,The maximum radiated power of radar i is represented,For radar i with Channel propagation impairments between target, wherein,It is i-th transmitter antenna gain (dBi) of radar,It is i-th reception of radar Antenna gain,It is the RCS of relative i-th radar of target, λ is radar emission signal wavelength, R_iFor i-th radar and target it Between distance；N_tIt is the number of radar in system； Wherein, c_i,jRepresent the cross-correlation coefficient between radar i and radar j, σ²It is system noise power, p_jIt is the transmission power of radar j Value,Represent the channel propagation impairments between radar i and radar j, d_i,jRepresent radar i with The distance between radar j, b_iIt is penalty factor, whenWhen, b_iKeep constant, whenWhen,WhenWhen,

4th, by utility function u_i(p_i,p_-i) to radiant power p_iFirst-order partial derivative is sought, and makes it be equal to zero：

To determine the transmission power of each radarBy the utility function u in (1) formula_i(p_i,p_-i) to radiation work( Rate p_iSeek first-order partial derivative, and make it be equal to zero, it is as follows：

5th, design can solve nonlinear equationNewton iterative：

By solving formula (2), the radiant power of each radar can be obtainedIteration expression formula is：

Wherein：It is the radar i transmission power levels that nth iteration is calculated,It is (n+1)th thunder of iterative calculation Up to i transmission power levels,For the radar i Signal to Interference plus Noise Ratio values that nth iteration is calculated；Through iterative calculation, try to achieve and meet target acquisition SINR scopesAnd make one group of minimum radiant power allocation result of Radar Network System total radiant powerMake It is optimal solution, and finally determines the total radiant power of system, each radar emission performance number of gained is with radio frequency Stealth Fighter Radar network composite power distribution result.

Claims (1)

1. a kind of radar network composite Poewr control method based on non-cooperative game, it is characterised in that comprise the steps of：

(1) channel propagation impairments between each radar and target in Radar Network System are obtained, its mathematical description is：

$h_{i,i}=\frac{G_i^t{G}_i^r{\mathrm{\σ}}_i^{RCS}{\mathrm{\λ}}^2}{{\left(4\mathrm{\π}\right)}^3{R}_i^4},i=1,2,...,N_t$

Wherein,It is i-th transmitter antenna gain (dBi) of radar,It is i-th receiving antenna gain of radar,It is target With respect to i-th RCS of radar, λ is radar emission signal wavelength, R_iFor between i-th radar and target away from From N_tIt is radar number in system；

(2) according to the investigative range for specifying SINRWherein：It is Signal to Interference plus Noise Ratio SINR value lower limit,It is letter It is dry to make an uproar than the SINR value upper limit, set up the radar network composite Power control model based on non-cooperative game：

$\left\{\begin{array}{cc}\underset{\left\{p_i,i=1,\mathrm{...},N_t\right\}}{\max }& u_i\left(p_i,p_{-i}\right)=\arctan \left(1+{\mathrm{\γ}}_i\right)+b_i{h}_{i,i}\ln \left(p_i^{\max }-p_i\right),\\ s.t.:& {\mathrm{\γ}}_{th}^{\min }\≤{\mathrm{\γ}}_i\≤{\mathrm{\γ}}_{th}^{\max },i=1,\mathrm{...},N_t\\ & 0\≤p_i\≤p_i^{\max },i=1,\mathrm{...},N_t\end{array}\right.$

Wherein, s.t. represents optimization object function " being limited to " following restrictive condition, u_i(p_i,p_-i) it is the utility function of radar i, p_iIt is the transmission power level of radar i, p_-iRepresent the radiant power of every other radar in the external system except radar i, b_iIt is punishment The factor,Represent the maximum radiated power of radar i, i-th Signal to Interference plus Noise Ratio γ of radar_iCan be represented by the following formula：

${\mathrm{\γ}}_i=\frac{h_{i,i}{p}_i}{\underset{j=1,j\≠i}{\overset{N_t}{\Σ}}{c}_{i,j}{h}_{i,j}{p}_j+{\mathrm{\σ}}^2},i=1,2,...,N_t$

Wherein, c_i,jRepresent the cross-correlation coefficient between radar i and radar j, σ²It is system noise power, p_jIt is the transmitting of radar j Performance number,Represent the channel propagation impairments between radar i and radar j, d_i,jRepresent thunder Up to the distance between i and radar j, b_iIt is penalty factor, whenWhen, b_iKeep constant, when When,WhenWhen,

(3) by utility function u_i(p_i,p_-i) to radiant power p_iSeek first-order partial derivative：

$\frac{\∂u_i\left(p_i,p_{-i}\right)}{\∂p_i}=\frac{h_{i,i}}{\underset{j=1,j\≠i}{\overset{N_t}{\mathrm{\Σ}}}{c}_{i,j}{h}_{i,j}{p}_j+{\mathrm{\σ}}^2}\frac{1}{1+{\left(1+{\mathrm{\γ}}_i\right)}^2}-\frac{b_i{h}_{i,i}}{p_i^{\max }-p_i}$

Wherein：u_i(p_i,p_-i) it is the utility function of radar i；

(4) by orderThe radiant power iteration expression formula of each radar is in acquisition Radar Network System：

$p_i^{\left(n+1\right)}=\left\{\begin{array}{cc}\sqrt{\frac{p_i^{\max }-p_i}{b_i{h}_{i,j}}\frac{p_i^{\left(n\right)}}{{\mathrm{\&gamma;}}_i^{\left(n\right)}}-{\left(\frac{p_i^{\left(n\right)}}{{\mathrm{\&gamma;}}_i^{\left(n\right)}}\right)}^2}-\frac{p_i^{\left(n\right)}}{{\mathrm{\&gamma;}}_i^{\left(n\right)}},& 0<p_i^{\left(n+1\right)}<p_i^{\max }\\ p_i^{\max },& p_i^{\left(n+1\right)}\&GreaterEqual;p_i^{\max }\end{array}\right.$

Wherein：It is the radar i transmission power levels that nth iteration is calculated,It is the radar i hairs of (n+1)th iterative calculation Penetrate performance number,For the radar i Signal to Interference plus Noise Ratio values that nth iteration is calculated.